Electronic and micromechanical devices are formed by patterning successive layers on a substrate using lithography. The patterns are formed by applying a layer of photoresist to a surface. Light is then passed through a patterned imaging plate, such as a mask or reticle, to expose the photoresist in patterns that correspond to the desired features on the substrate. A developer is applied and the photoresist is etched away leaving only the features in a pattern corresponding to the pattern on the mask. As the size of the features, such as parts of transistors, decreases, there are more features on the same size mask and the mask designs becomes more complex.
For very small features aggressive Optical Proximity Correction (OPC) or Inverse Lithography (ILT) is used when designing a mask in order to achieve a sufficiently high resolution to produce the small features. These mask design technologies can result in mask layouts that cannot be manufactured using conventional mask manufacturing technologies. One limitation of current mask making tools is a restriction on the number of shots used to make the mask. Shots are rectangles that the mask making tool uses to transfer geometry onto the mask. The restrictions can come in the form of total number of shots, shot density or total write time which is directly related to total shots.
Curved lines in particular have a large number of shots typically making them unmanufacturable. To manufacture a curve, the mask preprocessing tool fractures the mask layout into a large number of small rectangular tiles meaning that the curve has a very high shotcount. In addition, an aggressive mask design may not obey other mask making constraints like minimum edge to edge or corner to corner distances.